# cirq.DensePauliString

An immutable string of Paulis, like `XIXY`, with a coefficient.

Inherits From: `BaseDensePauliString`, `Gate`

A `DensePauliString` represents a multi-qubit pauli operator, i.e. a tensor product of single qubits Pauli gates (including the `cirq.IdentityGate`), each of which would act on a different qubit. When applied on qubits, a `DensePauliString` results in `cirq.PauliString` as an operation.

Note that `cirq.PauliString` only stores a tensor product of non-identity `cirq.Pauli` operations whereas `cirq.DensePauliString` also supports storing the `cirq.IdentityGate`.

For example,

````dps = cirq.DensePauliString('XXIY')`
`print(dps) # 4 qubit pauli operator with 'X' on first 2 qubits, 'I' on 3rd and 'Y' on 4th.`
`+XXIY`
`ps = dps.on(*cirq.LineQubit.range(4)) # When applied on qubits, we get a `cirq.PauliString`.`
`print(ps) # Note that `cirq.PauliString` only preserves non-identity operations.`
`X(q(0))*X(q(1))*Y(q(3))`
```

This can optionally take a coefficient, for example:

````dps = cirq.DensePauliString("XX", coefficient=3)`
`print(dps) # Represents 3 times the operator XX acting on two qubits.`
`(3+0j)*XX`
`print(dps.on(*cirq.LineQubit.range(2))) # Coefficient is propagated to `cirq.PauliString`.`
`(3+0j)*X(q(0))*X(q(1))`
```

If the coefficient has magnitude of 1, the resulting operator is a unitary and thus is also a `cirq.Gate`.

Note that `DensePauliString` is an immutable object. If you need a mutable version of dense pauli strings, see `cirq.MutableDensePauliString`.

`pauli_mask` A specification of the Pauli gates to use. This argument can be a string like "IXYYZ", or a numeric list like [0, 1, 3, 2] with I=0, X=1, Y=2, Z=3=X|Y.

The internal representation is a 1-dimensional uint8 numpy array containing numeric values. If such a numpy array is given, and the pauli string is mutable, the argument will be used directly instead of being copied.

`coefficient` A complex number. Usually +1, -1, 1j, or -1j but other values are supported.

`coefficient` A complex coefficient or symbol.
`pauli_mask` A 1-dimensional uint8 numpy array giving a specification of Pauli gates to use.

## Methods

### `controlled`

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Returns a controlled version of this gate. If no arguments are specified, defaults to a single qubit control.

Args
`num_controls` Total number of control qubits.
`control_values` Which control computational basis state to apply the sub gate. A sequence of length `num_controls` where each entry is an integer (or set of integers) corresponding to the computational basis state (or set of possible values) where that control is enabled. When all controls are enabled, the sub gate is applied. If unspecified, control values default to 1.
`control_qid_shape` The qid shape of the controls. A tuple of the expected dimension of each control qid. Defaults to `(2,) * num_controls`. Specify this argument when using qudits.

Returns
A `cirq.Gate` representing `self` controlled by the given control values and qubits. This is a `cirq.ControlledGate` in the base implementation, but subclasses may return a different gate type.

### `copy`

View source

Returns a copy with possibly modified contents.

Args
`coefficient` The new coefficient value. If not specified, defaults to the current `coefficient` value.
`pauli_mask` The new `pauli_mask` value. If not specified, defaults to the current pauli mask value.

Returns
A copied instance.

### `eye`

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Creates a dense pauli string containing only identity gates.

Args
`length` The length of the dense pauli string.

### `frozen`

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A `cirq.DensePauliString` with the same contents.

### `mutable_copy`

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A `cirq.MutableDensePauliString` with the same contents.

### `num_qubits`

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The number of qubits this gate acts on.

### `on`

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Returns an application of this gate to the given qubits.

Args
`*qubits` The collection of qubits to potentially apply the gate to.

Returns: a `cirq.Operation` which is this gate applied to the given qubits.

### `on_each`

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Returns a list of operations applying the gate to all targets.

Args
`*targets` The qubits to apply this gate to. For single-qubit gates this can be provided as varargs or a combination of nested iterables. For multi-qubit gates this must be provided as an `Iterable[Sequence[Qid]]`, where each sequence has `num_qubits` qubits.

Returns
Operations applying this gate to the target qubits.

Raises
`ValueError` If targets are not instances of Qid or Iterable[Qid]. If the gate qubit number is incompatible.
`TypeError` If a single target is supplied and it is not iterable.

### `one_hot`

View source

Creates a dense pauli string with only one non-identity Pauli.

Args
`index` The index of the Pauli that is not an identity.
`length` The total length of the string to create.
`pauli` The pauli gate to put at the hot index. Can be set to either a string ('X', 'Y', 'Z', 'I'), a cirq gate (`cirq.X`, `cirq.Y`, `cirq.Z`, or `cirq.I`), or an integer (0=I, 1=X, 2=Y, 3=Z).

### `sparse`

View source

A `cirq.PauliString` version of this dense pauli string.

Args
`qubits` The qubits to apply the Paulis to. Defaults to `cirq.LineQubit.range(len(self))`.

Returns
A `cirq.PauliString` with the non-identity operations from this dense pauli string applied to appropriate qubits.

Raises
`ValueError` If the number of qubits supplied does not match that of this instance.

### `tensor_product`

View source

Concatenates dense pauli strings and multiplies their coefficients.

Args
`other` The dense pauli string to place after the end of this one.

Returns
A dense pauli string with the concatenation of the paulis from the two input pauli strings, and the product of their coefficients.

### `validate_args`

View source

Checks if this gate can be applied to the given qubits.

By default checks that:

• inputs are of type `Qid`
• len(qubits) == num_qubits()
• qubit_i.dimension == qid_shape[i] for all qubits

Child classes can override. The child implementation should call `super().validate_args(qubits)` then do custom checks.

Args
`qubits` The sequence of qubits to potentially apply the gate to.

Raises
`ValueError` The gate can't be applied to the qubits.

### `with_probability`

View source

Creates a probabilistic channel with this gate.

Args
`probability` floating point value between 0 and 1, giving the probability this gate is applied.

Returns
`cirq.RandomGateChannel` that applies `self` with probability `probability` and the identity with probability `1-p`.

### `wrap_in_linear_combination`

View source

Returns a LinearCombinationOfGates with this gate.

Args
`coefficient` number coefficient to use in the resulting `cirq.LinearCombinationOfGates` object.

Returns
`cirq.LinearCombinationOfGates` containing self with a coefficient of `coefficient`.

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### `__call__`

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Call self as a function.

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### `__truediv__`

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I_VAL `0`
X_VAL `1`
Y_VAL `2`
Z_VAL `3`

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